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SUMMARY:Daniel Kriz (MIT)
DTSTART:20201214T200000Z
DTEND:20201214T213000Z
DTSTAMP:20260422T220226Z
UID:STAGE/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/20/">D
 work's $p$-adic proof of rationality\, continued</a>\nby Daniel Kriz (MIT)
  as part of STAGE\n\n\nAbstract\nWe will go over the main steps of Dwork's
  argument in detail. First\, we will construct a splitting function for th
 e standard additive character and show it has good convergence properties 
 using Dwork's lemma. Next we will establish the "analytic Lefschetz fixed 
 point formula" by studying the trace of this splitting function acting on 
 $p$-adic Banach spaces of power series. Finally\, we will show this analyt
 ic fixed point formula implies the zeta-function is the ratio of two entir
 e functions\, and conclude with a general rationality criterion for $p$-ad
 ic power series that implies the zeta-function is rational. \n\n\nReferenc
 e: <a href="https://link.springer.com/book/10.1007/978-1-4612-1112-9">Kobl
 itz\, p-adic numbers\, p-adic analysis\, and zeta-functions</a>\, whatever
  remains of Chapter V after the first lecture.\n
LOCATION:https://researchseminars.org/talk/STAGE/20/
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